Interaction of family SES with children’s genetic propensity for cognitive and noncognitive skills: No evidence of the Scarr-Rowe hypothesis for educational outcomes

This study examines the role of genes and environments in predicting educational outcomes. We test the Scarr-Rowe hypothesis, suggesting that enriched environments enable genetic potential to unfold, and the compensatory advantage hypothesis, proposing that low genetic endowments have less impact on education for children from high socioeconomic status (SES) families. We use a pre-registered design with Netherlands Twin Register data (426 ≤ Nindividuals ≤ 3875). We build polygenic indexes (PGIs) for cognitive and noncognitive skills to predict seven educational outcomes from childhood to adulthood across three designs (between-family, within-family, and trio) accounting for different confounding sources, totalling 42 analyses. Cognitive PGIs, noncognitive PGIs, and parental education positively predict educational outcomes. Providing partial support for the compensatory hypothesis, 39/42 PGI × SES interactions are negative, with 7 reaching statistical significance under Romano-Wolf and 3 under the more conservative Bonferroni multiple testing corrections (p-value < 0.007). In contrast, the Scarr-Rowe hypothesis lacks empirical support, with just 2 non-significant and 1 significant (not surviving Romano-Wolf) positive interactions. Overall, we emphasise the need for future replication studies in larger samples. Our findings demonstrate the value of merging social-stratification and behavioural-genetic theories to better understand the intricate interplay between genetic factors and social contexts.


Literature review
Table A1: Literature review of studies that investigate the interaction between genetic propensity to educational attainment, cognitive and noncognitive skills and socioeconomic background using molecular data.Note: PGI EA3: Polygenic index for educational attainment release 3 (Lee et al., 2018).PGI EA2: Polygenic index for educational attainment release 2 (Rietveld et al., 2013).Previous studies are ordered in chronological order.

Differences between the pre-registered study and the final version
Here we list and motivate a few differences between the pre-registration and the final version: 1. Regarding adult educational attainment, we restrict the analysis to those born from 1980 instead of taking the overall available sample while conducting robustness checks on the subsample born before 1980 (see below).This decision was motivated by having comparable samples of the historical period and educational system between the young and adult Netherlands Twin Study cohorts since the latter has a year of birth distribution ranging from 1909 to 2001. 2. We do not look at teachers' recommendations for the type of secondary school attended (at age 12) as an additional outcome due to its many missing observations.We thus decided to exclude it since we already included the actual academic track attended by the child.3. We also added the genetic testing platform as a control variable in all models, as it can be a potential confounder.4. In the pre-registration, we state the intention to perform a power analysis before data analyses to discard those underpowered outcomes/analytical samples and avoid the likelihood of observing false positives or not detecting true positives.Instead, we performed a post-hoc power analysis.5. We estimated models accounting for the prediction hypothesis in the pre-registration (i.e., the impact of the PGI for cognitive and noncognitive skills on educational outcomes).However, for the sake of brevity in the final version of the paper, we decided to focus mainly on the Scarr-Rowe and compensatory advantaged hypotheses.6. Regarding the theoretical expectations, although we discussed and speculated about the implications of the outcomes' timing for the main findings and how future research might address it, we did not specify or test any hypotheses about the timing of the outcomes.More specifically, in the pre-registration, we expect that: -The association between cognitive and noncognitive PGI would increase with age; -The GxE would be stronger for school grades than CITO scores; -The GxE would be stronger for tracking than CITO scores; -The GxE would be stronger for later outcomes than earlier.

Samples characteristics and descriptive statistics
The following are the main criteria used to select our analytical samples.We selected all children or adult participants in the NTR with the available: 1. Genotypic data; 2. Information on at least one of the following educational outcomes in all birth cohorts: school grades in numeracy and literacy, CITO at age 12, type of secondary school attended from age 12, and educational attainment; 3. Information on parental SES (i.e., parent's education).

Power analysis for an R2 test in a multiple linear regression
We used the 'power rsquared' command in STATA to estimate the minimum incremental R2 that would yield a statistically significant result using an F-test.This command allows us to determine the smallest detectable increase in R2 given a predefined sample size and a specified power level of 0.8.For each outcome and design, we defined the R2 of the reduced model as 0.05 and the number of control variables as 11 before estimating the minimum incremental R2 required.The 'power rsquared' command then calculated the minimum detectable incremental R2, representing the difference between the R2 of the full model (R2_F) and that of the reduced model (R2_R).
In the between-family analysis, the minimum detectable value for the R2 difference ranges from 0.002 to 0.006, varying by sample.To achieve a statistical power of 80% and a significance level of 5%, our sample sizes enable us to detect incremental R2 associations of 0.20% in the mathematics and reading samples at ages 7 and 10, 0.30% in the CITO sample, 0.20% in tracking sample, and 0.60% in the educational attainment sample (see Table A13 and Figure A1).We conclude that by including an additional tested covariate (i.e., the interaction) in each sample, assuming a power of 80%, it is possible to confidently observe a significant change in the model's explanatory power.In the within-family analysis, the minimum detectable value for the R2 difference ranges from 0.003 to 0.013.Therefore, if we require a statistical power of 80% and a significance level of 5%, our sample sizes will allow us to detect associations with an incremental R2 of 0.35% in the mathematics and reading sample at age 7, 0.33% in the mathematics and reading sample at age 10, 0.50% in the CITO sample, 0.37% in secondary tracking sample, and 1.17% in the educational attainment sample (see Table A14 and Figure A2).Again, the minimum detectable R2 is small -except for educational attainment -which suggests that including the interaction coefficient in the model allows capturing really small changes in the explanatory power of the model.Finally, in the trio analysis, the minimum detectable value for the R2 difference ranges from 0.004 to 0.013 (see Table A15 and Figure A3).This means that if we require a statistical power of 80% and a significance level of 5%, our sample sizes will allow us to detect associations with an incremental R2 of 0.40% in the mathematics and reading sample at age 7, 0.36% in the mathematics and reading sample at age 10, 0.60% in the CITO sample, 0.50% in the tracking sample and 1.3% in the educational attainment sample.In line with the within-family analysis, the minimum detectable R2 is generally small -except for educational attainment.Thus, including the interaction coefficient in the model enables the detection of even minor variations in the model's explanatory power.Note: R2_F: R2 of the full model, R2_R: R2 of the reduced model.
Figure A3: Estimated R-squared for multiple linear regression in the trio analysis

Post-hoc power analysis using Monte Carlo simulation
We also conduct a post-hoc power analysis using Monte Carlo simulations.Power estimates are derived from 1,000 Monte Carlo simulations with alpha set to 0.05 for each outcome in each design (between, within and trio).Statistical power is the probability of detecting a significant result given that the alternative (here G×E) hypothesis is true.We implement the following procedure:

Results
The power analysis indicates a potential issue with low statistical power in our study, particularly affecting certain outcomes such as grades, the within-family design, and analyses using the noncognitive PGI.However, in the between-family analysis, the power analysis confirms sufficient statistical power for the outcomes where statistically significant results were observed (see Tables A16 and A17).These outcomes, which exhibited higher statistical power, are tracking and educational attainment.Moreover, the statistical power is also higher for CITO and mathematics at age 10 than for other outcomes.This highlights the robustness of our findings in detecting those statistically significant interactions.

Replicability
We created a STATA program (see ados: powersimuB and powersimuWI) and then ran the program to conduct the power analysis using Monte Carlo simulation (see dofiles: 9_power_analysis_PGICOG and 9_power_analysis_PGINCOG in the replication package).See also https://www.stata.com/support/faqs/statistics/power-by-simulation/

Multiple testing
Since the large number of outcomes included in this paper (seven in total), we have applied formal corrections to the p-values of our results to account for multiple comparisons.We used two procedures.First, we apply Bonferroni correction.For each PGI, we performed the same analysis on 7 outcomes, so the adjusted p-value threshold for significance is 0.05/7 = 0.007.Then, we implement the bootstrap procedure for multiple testing corrections introduced by Romano and Wolf (2005), further detailed in Romano and Wolf (2016) and Clarke et al. (2020).Specifically, the Romano-Wolf correction controls the family-wise error rate (FWER), which is the probability of incorrectly rejecting at least one true null hypothesis in a family of hypotheses under investigation.This method yields adjusted p-values robust against inflated Type I error rates and accommodates the dependence structure among the test statistics.
Tables A18-A19 present the original p-values and Romano-Wolf corrected p-values for each test.They also indicate whether the outcome p-values are under the Bonferroni threshold for the interaction between family SES and the PGI for cognitive skills (Table A18) or noncognitive skills (Table A19).Overall, 7 out of 10 statistically significant negative interactions survive the Romano-Wolf correction (4 for the cognitive PGI and 3 for the noncognitive PGI), while the only significant positive interaction in the within-family analysis does not.Since Bonferroni is a more conservative approach, we only find robust evidence for a negative GxE interaction in the between-family design for tracking (cognitive skills' PGI) and educational attainment (cognitive and noncognitive skills' PGIs)

Between-family design
Figure A4: Logistic regression models for dichotomous outcomes variables in the between-family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for cognitive skills (average marginal effect, at 95 percent confidence interval) Note: Average marginal effect (AME).Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).For this robustness check, school grades are dichotomized.

Within-family design
Figure A6: Logistic regression models for dichotomous outcomes variables in the trio samples (controlling for parents' PGI) for the interaction between family SES and PGI for cognitive skills (average marginal effect, at 95 percent confidence interval) Note: Average marginal effect (AME).Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).For this robustness check, school grades are dichotomised.
Figure A7: Logistic regression models for dichotomous outcomes variables in the trio samples (controlling for parents' PGI) for the interaction between family's SES and PGI for noncognitive skills (average marginal effect, at 95 percent confidence interval) Note: Average marginal effect (AME).Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).For this robustness check, school grades are dichotomised.

Between-family design
Table A24: OLS regression models with PGI in terciles in the between-family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for cognitive skills on our not dichotomous variables (i.e., CITO and school grades p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).
Figure A8: OLS regression models with PGI in terciles in the between-family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for cognitive skills on our not dichotomous variables (i.e., CITO and school grades).Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).
Table A25: OLS regression models with PGI in terciles in the between-family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for noncognitive skills on our not dichotomous variables (i.e., CITO and school grades p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Trio design
Figure A10: OLS regression models with PGI in terciles in the trio samples for the interaction between family's SES and PGI for cognitive skills on our not dichotomous variables (i.e., CITO and school grades).
Figure A11: OLS regression models with PGI in terciles in the trio samples for the interaction between family's SES and PGI for non-cognitive skills on our not dichotomous variables (i.e., CITO and school grades).Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Between-family design
Figure A12: Logistic regression models for dichotomous outcomes variables and with the PGI in terciles in the between family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for cognitive skills (average marginal effect, at 95 percent confidence interval) Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).
Figure A13: Logistic regression models for dichotomous outcomes variables and with the PGI in terciles in the between family samples (without controlling for parents' PGI) for the interaction between family's SES and PGI for non-cognitive skills (average marginal effect, at 95 percent confidence interval) Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Trio design
Figure A14: Logistic regression models for dichotomous outcomes variables (i.e., academic tracking and educational attainment) and with the PGI in terciles in the trio samples (controlling for parents' PGI) for the interaction between family's SES and PGI for cognitive skills (average marginal effect, at 95 percent confidence interval) Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).
Figure A15: Logistic regression models for dichotomous outcomes variables (i.e., academic tracking and educational attainment) and with the PGI in terciles in the trio samples (controlling for parents' PGI) for the interaction between family's SES and PGI for non-cognitive skills (average marginal effect, at 95 percent confidence interval) Controls are included.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).In this section, we first repeat the analysis for educational attainment using different samples.Specifically, we compare the main results (those born after 1980) with the results obtained looking also at those born before 1980 and then only to those born before 1980.

Educational attainment as continuous outcome
We repeat the analysis without dichotomising educational attainment by using it in four categories as originally provided by NTR (1: primary school only, lower vocational school and lower secondary school, intermediate vocational school and intermediate or higher secondary school, higher vocational school and university).0.133 0.143 0.0911 Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Figure A1 :
Figure A1: Estimated R-squared for multiple linear regression in the between-family analysis

Figure A2 :
Figure A2: Estimated R-squared for multiple linear regression in the within-family analysis

Table A2 :
Comparison between the population and the NTR (YNTR and ANTR samples) by full and analytical samples

Table A3 :
Missing data description for the YNTR and ANTR datasets

Table A6 :
OLS and LPM (academic tracking and educational attainment)regressions to test the interaction between children's cognitive and noncognitive PGI and family SES on educational outcomes.

Table A7 :
Family-fixed effect regressions to test the association between children's cognitive and noncognitive PGI and educational outcomes.

Table A9 :
OLS (mathematics, reading and CITO) and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and noncognitive PGI and educational outcomes using the sample of the trio-design, without controlling for family SES and parents cognitive and noncognitive PGI.Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A10 :
OLS (mathematics, reading and CITO)and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and noncognitive PGI and educational outcomes using the sample of the trio-design, controlling for family SES and not for parents cognitive and noncognitive PGI.

Table A11 :
OLS (mathematics, reading and CITO)and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and noncognitive PGI and educational outcomes using the sample of the trio-design, controlling for family SES and for parents cognitive and noncognitive PGI.

Table A12 :
OLS and LPM (academic tracking and educational attainment)regressions to test the interaction between children's PGI for cognitive and noncognitive skills and family SES on educational outcomes.

Table A13 :
Estimated R-squared for multiple linear regression in the between-family analysis

Table A14 :
Estimated R-squared for multiple linear regression in the within-family analysis Note: R2_F: R2 of the full model, R2_R: R2 of the reduced model.

Table A15 :
Estimated R-squared for multiple linear regression in the trio analysis

Table A16 :
Statistical power using the PGI for cognitive skills

Table A18 :
Corrections for multiple hypothesis testing by outcome and design for the interaction between family SES and PGI for cognitive skills Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs, Platform, gender and birth year.We also include covariatesenvironment (family's' SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A21 :
Family-fixed effect regressions to test the interaction between children's cognitive and noncognitive PGI and family SES on educational outcomes controlling also for gender and birth year.

Table A22 :
OLS and LPM (academic tracking and educational attainment) regressions to test the interaction between children's PGI for cognitive and noncognitive skills and family SES on educational outcomes controlling also for gender and birth year.

Table A23 :
Logistic regression models for dichotomous outcomes variables in the within-samples for the interaction between family SES and PGI for cognitive and noncognitive skills at 95 percent confidence interval

Table A26 :
OLS regression models with PGI in terciles in the trio samples for the interaction between family's SES and PGI for cognitive skills on our not dichotomous variables (i.e., CITO and school grades).

Table A27 :
OLS regression models with PGI in terciles in the trio samples for the interaction between family's SES and PGI for non-cognitive skills on our not dichotomous variables (i.e., CITO and school grades).

Table A28 :
OLS (mathematics, reading and CITO)and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and non-cognitive PGI and educational outcomes without including family SES.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A29 :
OLS (mathematics, reading and CITO) and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and non-cognitive PGI and educational outcomes including family SES.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A30 :
OLS (mathematics, reading and CITO) and LPM (academic tracking and educational attainment) regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A31 :
OLS (mathematics, reading and CITO) and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and non-cognitive PGI and educational outcomes using the sample of the trio-design, controlling for family SES but without parents cognitive and non-cognitive PGI.

Table A32 :
OLS (mathematics, reading and CITO) and LPM (academic tracking and educational attainment) regressions to test the association between children's cognitive and non-cognitive PGI and educational outcomes using the sample of the trio-design, controlling for family SES and parents cognitive and non-cognitive PGI.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A33 :
OLS (mathematics, reading and CITO)and LPM (academic tracking and educational attainment) regressions to test the interaction between children's cognitive and non-cognitive PGI and family's SES using the sample of the trio-design, controlling for family SES and parents cognitive and non-cognitive PGI.

Table A34 :
LPM regressions to test the association between children's cognitive and non-cognitive PGI and educational attainment controlling for family SES in the between-family design in the three different samples Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A35 :
LPM regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES in the between-family design in the three different samples Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A36 :
Family-fixed effect regressions to test the association between children's cognitive and non-cognitive PGI on educational attainment in the within-family design in the three different samples Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A37 :
Family-fixed effect regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES in the within-family design in the three different samples Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A38 :
LPM regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES in the trio design in the three different samples Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.

Table A39 :
LPM regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES in the trio design in the three different samples

Table A40 :
OLS and LPM (academic tracking and educational attainment) regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES on educational outcomes in the between-family analysis.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A41 :
Family-fixed effect regressions to test the interaction between children's cognitive and non-cognitive PGI and family SES on educational outcomes in the within-family analysis.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A42 :
OLS and LPM (academic tracking and educational attainment) regressions to test the interaction between children's cognitive PGI and family SES on educational outcomes in the trio analysis.Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A43 :
LPM regression models to test the interaction between children's cognitive and non-cognitive PGI and family SES in the between design in the three different samples and using educational attainment not dichotomized Note: Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A44 :
Family-fixed effect regressions to test the interaction between children's non-cognitive PGI and family SES in the within-family design in the three different samples and using educational attainment not dichotomized Robust standard errors in parentheses.Two-tailed t-test: + p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.000.Controls included but not reported above: first 10 PCs and Platform.We also include covariates-environment (family SES) and covariates-gene (PGI) interaction (Keller, 2014).

Table A45 :
LPM regression models to test the interaction between children's cognitive and non-cognitive PGI and family SES in the trio design in the three different samples and using educational attainment not dichotomized